Yea LP's are not great with square waves but 44.1 digital is so bandwidth limited it does not do very well with higher frequency square waves either. My point is while I do understand how square waves can be very useful to quickly troubleshoot issues with electronics using them to determine how something is going to sound playing back actual music is not so clear cut.
Square wave comparison arguments have an element of bogusness in them. The components of 'high frequency square waves' -- higher order harmonics -- that makes them square, are not heard by human ears.
What's important is how well the part that humans CAN hear, is reproduced distortion free. Put another way, you can fudge a lot of 'squareness' and humans won't hear a difference.